Horo-functions associated to atom sequences on the Wasserstein space

Abstract

On the Wasserstein space over a complete, separable, non-compact, locally compact length space, we consider the horo-functions associated to sequences of atomic measures. We show the existence of co-rays for any prescribed initial probability measure with respect to a sequence of atomic measures and show that co-rays are negative gradient curves in some sense. Some other fundamental results of this kind of functions are also obtained.